{"paper":{"title":"On the spectral moment of graphs with given clique number","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shuchao Li, Shuna Hu, Xixi Zhang","submitted_at":"2012-09-16T01:55:21Z","abstract_excerpt":"Let $\\mathscr{L}_{n,t}$ be the set of all $n$-vertex connected graphs with clique number $t$\\,($2\\leq t\\leq n)$. For $n$-vertex connected graphs with given clique number, lexicographic ordering by spectral moments ($S$-order) is discussed in this paper. The first $\\sum_{i=1}^{\\lfloor\\frac{n-t-1}{3}\\rfloor}(n-t-3i)+1$ graphs with $3\\le t\\le n-4$, and the last few graphs, in the $S$-order, among $\\mathscr{L}_{n,t}$ are characterized. In addition, all graphs in $\\mathscr{L}_{n,n}\\bigcup\\mathscr{L}_{n,n-1}$ have an $S$-order; for the cases $t=n-2$ and $t=n-3$ the first three and the first seven gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3455","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}